多获胜者选举：正当代表性、策略无偏性与规避风险的真实性
Multi-Winner Elections: Justified Representation, Strategyproofness, and Risk-Avoiding Truthfulness
浏览论文内容
中文总结 AI 辅助
本文针对选民策略性提交选票的多获胜者选举，证明不存在满足正当代表性的策略无偏机制，转而采用RAT度分析发现标准比例规则表现较差。
中文摘要 AI 辅助
我们研究选民策略性提交选票时基于认可的多获胜者选举中的正当代表性（JR）。我们证明，不存在能输出JR委员会的策略无偏机制，即便该机制可随机化且仅需事前策略无偏性，该不可能性结果对任何固定的选民单调效用函数均成立。此外，我们的不可能性结果在更受限的场景下依然成立，例如仅允许选择少于k名候选人、仅含4名候选人与3名选民的场景。受负面结果启发，我们转而研究选民部分信息下更弱的策略无偏保证，采用Hartman、Segal-Halevi与Tao（EC'25）提出的RAT度概念，即操纵者实施安全且有利的偏离前必须知晓的其他选民信息数量。标准比例规则，如贪婪认可投票、比例认可投票（PAV）及等额份额法（MES），在RAT度度量下表现不佳（RAT度较低）。
英文摘要
We study approval-based multi-winner elections with Justified Representation (JR) when voters strategically report their ballots. We prove that there does not exist a strategy-proof mechanism that outputs JR committees, even when the mechanism can be randomized and only Ex-Ante strategyproofness is required. The impossibility already holds with three voters, four candidates, and target committee size three, even when the mechanism may select fewer than three candidates. It applies to every common strictly increasing cardinality-based utility function and scales to every target size $k\geq3$, every number of voters divisible by $k$, and every candidate-set size at least $k+1$. Motivated by our negative results, we then ask for weaker strategy-proof guarantees under voters' partial information. We use the notion of Risk-Avoiding Truthfulness and its RAT-Degree proposed by Hartman, Segal-Halevi, and Tao (EC'25), the number of other voters whose information a manipulator must know before a safe and profitable deviation is possible. Standard proportional rules, such as Greedy Approval Voting, Proportional Approval Voting, and the Method of Equal Shares, have poor performances under the RAT-Degree metric (with low RAT-Degrees). Finally, for $n$ voters, we construct a JR mechanism with RAT-Degree at least $n-5$, without a polynomial-time bound. We then use the same idea together with algebraic ballot encodings to obtain a polynomial-time JR mechanism with RAT-Degree at least $n-7$. When voters also have immutable private identifiers and both the identifiers and ballots of unknown voters are unobserved, we obtain a polynomial-time JR mechanism with RAT-Degree at least $n-1$ for $2\le k<m$. This degree is exactly $n-1$ when $k\ge3$ and $k$ divides $n$.
发表机构
- University of Toronto（多伦多大学）
- Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。
